The cost the company budget on average for a gallon of fuel across its operations is given by: Option D: $3.70
A random variable is usually taking some numerical information of each elementary event of the sample space . (map from sample space to real numbers). Its expected value is the best prediction value in most of the cases. It is the mean or average value of that random variable.
Supposing that the considered random variable is discrete, we get:
[tex]Mean = E(X) = \sum_{\forall x_i} f(x_i)x_i\\\\[/tex]
where [tex]x_i; \: \: i = 1,2,.. , n[/tex] is its n data values
and [tex]f(x_i)[/tex] probability of [tex]X = x_i[/tex]
Percent counts the number compared to 100 whereas probability counts it compare to 1.
So, if we have a%, that means for each 100, there are 'a' parts. If we divide each of them with 100, we get:
For each 1, there are a/100 parts.
Thus, 50% = 50/100 = 0.50 (in probability)
If assuming that X = Fuel cost per gallon, then
E(X) = Average fuel cost per gallon that the company should budget (its per gallon, means for a gallon)
Using the tabulated value given in the problem, we get:
[tex]Mean = E(X) = \sum_{\forall x_i} f(x_i)x_i\\\\\\\\E(X) = 3.10 \times 0.2 + 3.5 \times 0.3 + 4.05 \times 0.5 = 3.695 \approx 3.70[/tex] (in dollars)
(we converted percentage to probability).
Thus, the cost the company budget on average for a gallon of fuel across its operations is given by: Option D: $3.70
Learn more about expectation of a random variable here:
https://brainly.com/question/4515179
Answer:
D is the correct answer! ~Hope this helps!
Step-by-step explanation:
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